Digital focus lens system

ABSTRACT

Digital focus lens systems that can provide an optical system with a plurality of selectable focal powers are described. The systems may include a number of switchable elements, each of which is capable of being switched between a first state and a second state, whereby the states represent focal powers. The switchable elements may be arranged coaxially in a stack such that each of them may contribute to a cumulative focal power of the system. If, for example, the system includes two such switchable elements, four focal powers for the lens system may be selected by appropriate choice the states of each switchable element. Digital telescopes, cameras, microscopes, and other optical instruments may be implemented using such digital focus lens systems. Methods of fabricating switchable elements and methods of controlling digital lens systems are also disclosed.

This application claims the benefit of U.S. Provisional PatentApplication No. 60/395,849 filed Jul. 11, 2002, the entire disclosuresof which are incorporated herein by reference. This application is alsoa continuation-in-part of co-pending U.S. patent application Ser. No.10/029,399 filed Oct. 19, 2001, the entire contents of which areincorporated herein by reference.

FIELD OF THE INVENTION

This invention relates to optical components such as optical lenscomplexes and more specifically, to variable-focus lenses such as liquidcrystal lenses.

BACKGROUND OF THE INVENTION

Solid-state variable-focus lens systems are needed in a variety ofapplications such as in cameras deployed on aircraft and subjected tostrong acceleration forces. It is often desirable to have avariable-focus lens system that is compact and capable of solid-stateoperation; and further, one in which the number of possible states offocusing is an exponential function of the number of optical elements inthe system. Conventional variable-focus lens systems are bulky, requiremoving parts, or require numerous elements resulting in optical lossesand aberration of the images.

Thus, there is a need in the art, for a lens system that overcomes theabove disadvantages.

BRIEF DESCRIPTION OF THE DRAWINGS

The teachings of the present invention can be readily understood byconsidering the following detailed description in conjunction with theaccompanying drawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a digital focus lens system according to an embodiment ofthe present invention.

FIG. 2 shows another view of a digital focus lens system.

FIG. 3 shows yet another view of a digital focus lens system.

FIG. 4 shows yet another view of a digital focus lens system.

FIG. 5 shows another embodiment of a digital focus lens system.

FIG. 6 shows yet another embodiment of a digital focus lens system.

FIGS. 7A–7D are a sequence of cross-sectional schematic diagrams thatillustrate a method for fabricating the switchable elements of a digitalfocus lens system according to an embodiment of the invention.

FIG. 8 shows schematic diagram illustrating a method of controlling adigital focus lens system according to an embodiment of the invention.

FIG. 9 shows a digital focus lens system incorporated in a digitaltelescope according to an embodiment of the invention.

DESCRIPTION OF THE SPECIFIC EMBODIMENTS

Although the following detailed description contains many specificdetails for the purposes of illustration, anyone of ordinary skill inthe art will appreciate that many variations and alterations to thefollowing details are within the scope of the invention. Accordingly,the embodiments of the invention described below are set forth withoutany loss of generality to, and without imposing limitations upon, theclaimed invention.

According to an embodiment of the present invention digital focus lenssystem may include a stack of switchable lens elements. The stack mayinclude a plurality of optically transparent substrates symmetricallyspaced apart, optically transparent electrodes deposited on the surfacesof each substrate, polymer layers deposited on the electrodes, andliquid crystal (LC) layers filling the gaps between adjacent pairs ofpolymer layers. Each polymer layer may be spatially patterned to providea selected lens function having a selected focal length, and each istreated with alignment features to facilitate orientation of the LCmonomers. When a selected voltage is applied across adjacent pairs ofelectrodes, the refractive index of the LC layer positioned betweenthose electrodes is switched to a selected value and the focal lengthsof the polymer layers adjacent to the LC layer are modulated. Thus, eachgroup of electrode-polymer-LC-polymer-electrode layers may constitute adifferent switchable lens element where each can be switched between afirst state, having a first focal length, and a second state, having asecond focal length.

A control signal may be provided for selecting the states of theswitchable lens elements. For a stack of N switchable lens elements, thecontrol signal will include a digital word comprised of at least N bits.The control signal is demultiplexed and each bit used to modulate thevoltage applied to a corresponding switchable lens element. The state ofeach switchable lens element is thus controlled by a corresponding bitof the digital word.

The switchable lens elements can be stacked coaxially and can beswitched independently to either state. Thus, the system has a focallength that is determined by the instantaneous combination of states ofthe switchable lens elements. In the first state, the switchable lenselements may have identical focal lengths. In the second state, thefocal lengths of the switchable lens elements increase, following aprogression, similar to binary weighting, in which the focal length ofeach sequential switchable lens element in the stack increases by afactor of 2 from that of the previous element. For a system comprising astack of N switchable lens elements, the focal length can be selectedfrom a set of at least 2^(N) values. The system thus has a focal powerthat is a function of the digital word contained in the control signal.

Referring now to FIG. 1, a digital focus lens system according to anembodiment of the present invention is shown and indicated generally at110. System 110 employs a first optical module, M₁ (first module) 120.First module 120 incorporates a number of optical elements (elements)indicated schematically at 130. The individual elements 130 in themodule 140 are in optical communication with each other such that eachelement 130 in the module 140 may contribute to a cumulative opticalaffect. For example, the elements 130 may be oriented such that theoptical axes 140 of elements 130 are generally collinear with theoptical axis 150 of the system 110. Some or all of elements 130 may bepositioned in close proximity to adjacent elements. In this fashion, theelements in first module 120 may form a first stack of elements (firststack) 160. One or more of Elements 130 may be similar to thin lenseswhereby the standard thin lens approximation formulas may be applicableto portions of first stack 160 and/or first module 120. First module 120and/or first stack 160 may also be considered similar to a “lens group”,o to a “lens complex,” terms commonly used in the field of lens design.

At least one of elements 130 includes a first switchable element 170.First switchable element 170 may be activated between a number of uniquestates, where for each state, first switchable element 170 is capable ofperforming a unique optical transform (or filter function). Preferably,first switchable element 170 may be activated between two states,however, in general, any number of states may be utilized by firstswitchable element 170. Preferably, the transform performed by firstswitchable element 170 is similar to that of a thin lens. For example,first switchable element 170 may be activated into afirst-switchable-element first-state (FSE 0-state), having the propertyof an FSE 0-state focal length 180. Similarly, first switchable element170 may be activated into a first-switchable-element second-state (FSE1-state) having an FSE 1-state focal length 190. First Module 120 mayalso incorporate a second switchable element 200. Second switchableelement 200 may be activated into a second-switchable-elementfirst-state (SSE 0-state), having the property of an SSE 0-state focallength 210. Similarly, second switchable element 200 may be activatedinto a second-switchable-element second-state (SSE 1-state) having anSSE 1-state focal length 220. In this fashion, First Module 120 may alsoincorporate additional switchable elements 230. In this fashion, firstmodule 120 may incorporate a number of switchable elements, N, indicatedgenerally at 236 whereby each switchable element may be activatedbetween a first state (0-state) and a second state (1-state)corresponding to a first focal length and a second focal length,respectively. Examples of switchable elements 170, 200 include withoutlimitation liquid crystals (LCs), holographic optical elements,polymer-dispersed liquid crystals, nonlinear optical lenses,electro-optic elements, electro-optic lenses, LC lenses, LC prisms, LCgratings, LC shutters, LC aperture stops, LC irises, polymer dispersedliquid crystals, switchable holographic optical elements (HOEs),polarization rotators, isotropic, uniaxial, biaxial and/or otheranisotropic optical materials, deformable mirrors and deformablegratings, and micro-electro-mechanical systems (MEMS) and MEMS mirrors.Similarly, a second module 240 and third module 250, and in general, anynumber of additional modules (not shown), may be incorporated in system110.

Turning now to FIG. 2, a further description of the optical propertiesof a digital focus lens system according to an embodiment of the presentinvention is shown and indicated generally at 254. The same componentsas in FIG. 1 have the same assigned number as in FIG. 1. System 110includes a first module 120. First module 120 includes a first stack160. First stack 160 includes a number of elements 130. One or more ofelements 130 comprise a number of switchable elements, N, 236. For thepurpose of the indexing the N switchable elements 236, each switchableelement may be assigned a unique subscript number n, where n may bechosen from the set:nε{0,1 . . . N−1}.  Eq. 1

Each switchable element n may be switched between two specified states,however, in general, any number of states may be specified.

An impulse (or “state”) variable, δ_(m,n) (state), can be defined ascorresponding to the state of switchable element n in module m where

$\begin{matrix}{{\delta_{m,n}({state})} = \left\{ {\begin{matrix}0 & {0\text{-}{state}} \\1 & {1\text{-}{state}}\end{matrix}.} \right.} & {{Eq}.\mspace{14mu} 2}\end{matrix}$

For the remainder of this discussion, the parenthesis (state) will bedropped from the symbol δ_(m,n) for simplification. It follows that aδ_(m,n) will be specified for each switchable element n in module m.Also, it will be seen that δ_(m,n) is similar to delta functionscommonly used in the field of Fourier analysis.

By way of example, δ_(1,0), corresponding to the state of switchableelement 0 in module 1, may have the value δ_(m,n)=0 while the 0^(th)element is activated in the 0-state, and the value 1 while activated in1-state. Now, a switchable element focal length variable, f_(m,n)^(δm,n) is given to specify the focal length of switchable element n inmodule m. The parameters of f_(m,n) ^(δm,n) are: a first subscript mspecifying the module number; a second subscript n specifying theswitchable element number and a superscript δ_(m,n) specifying the stateof the n^(th) element in module m. It follows that a variable f_(m,n)^(δm,n) will be specified for each switchable element n in each modulem. As illustrated in FIG. 2, the 0-state and 1-state switchable elementfocal lengths of switchable element n=2 in module m=1 are identified byf_(1,2) ⁰ and f_(1,2) ¹, respectively. As a further example of thisnomenclature, the 0-state focal length of the first switchable element170 in the first module 120 will be referred to by the symbol f_(1,0) ⁰300. The 1-state focal length of the first switchable element 170 in thefirst module 120 will be referred to by the symbol f_(1,0) ⁰ 310.Similarly, the 0-state focal length of the second switchable element 200in the first module 120 will be referred to by the symbol f_(1,1) ⁰ 320.As a final example of the nomenclature, the 1-state focal length of thesecond switchable element 200 in the first module 120 will be referredto by the symbol f_(1,1) ¹ 330. Next, a module focal length, F_(m), 256is given for the focal length of a module where the module number isindicated by the subscript m. For example, F₁ 260 is the symbol for themodule focal length 256 of the first module 120, m=1. From the abovediscussion, it follows that, for the case of the switchable elementsbeing approximated as a stack of thin lenses (such when each element canbe approximated as a thin lens and each is in approximate contact withany adjacent elements) and the paraxial approximation applies to thestack, the module focal length, F_(m), can be expressed as

$\begin{matrix}{F_{m} = {\left( {\sum\limits_{n = 0}^{N - 1}\left( {\frac{\delta_{m,n}}{f_{m,n}^{1}} + \frac{1 - \delta_{m,n}}{f_{m,n}^{0}}} \right)} \right)^{- 1}.}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

Eq. 3 can be rearranged as

$\begin{matrix}{F_{m} = {\left\lbrack {\left( {\sum\limits_{n = 0}^{N - 1}\frac{1}{f_{m,n}^{0}}} \right) + {\sum\limits_{n = 0}^{N - 1}{\delta_{m,n}\left( {\frac{1}{f_{m,n}^{1}} - \frac{1}{f_{m,n}^{0}}} \right)}}} \right\rbrack^{- 1}.}} & {{Eq}.\mspace{14mu} 4}\end{matrix}$

In one embodiment of the invention, the N switchable elements in modulem may be constructed such that their 1-state focal lengths, f_(m,n) ¹,follow the mathematical form

$\begin{matrix}{f_{m,n}^{1} = \left( {\frac{2^{n}}{\Delta_{m}} + \frac{1}{f_{m,n}^{0}}} \right)^{- 1}} & {{Eq}.\mspace{14mu} 5}\end{matrix}$where Δ_(m) is a constant for module m, is independent of n, and has thedimension of length. Generally, however, in other embodiments of theinvention, f_(m,n) ¹ may be expressed by other mathematical forms.

Substituting Eq.5 into Eq. 4 gives

$\begin{matrix}{F_{m} = {\left\lbrack {\left( {\sum\limits_{n = 0}^{N - 1}\frac{1}{f_{m,n}^{0}}} \right) + {\frac{1}{\Delta_{m}}{\sum\limits_{n = 0}^{N - 1}{\delta_{m,n}2^{n}}}}} \right\rbrack^{- 1}.}} & {{Eq}.\mspace{14mu} 6}\end{matrix}$

Now it can be seen that the second summand term in Eq. 6 will have aunique value for each possible combination of states δ_(m,n) for the Nswitchable elements 236 in module m.

Neglecting the

$\frac{1}{\Delta_{m}}$factor in front of the summand term of Eq. 6, the combination ofpossible values for the summand define the set of integers

$\begin{matrix}{{\sum\limits_{n = 0}^{N - 1}{\xi_{n}2^{n}}} \in {\left\{ {0,{{1\mspace{11mu}\ldots\mspace{14mu} 2^{N}} - 1}} \right\}.}} & {{Eq}.\mspace{14mu} 7}\end{matrix}$

The summand of Eq. 7 can be replaced with a dimensionless indexingvariable, k,

where k represents any value of the set of integers corresponding to the2^(N) possible combinations of states for the N switchable elements inmodule m. Substituting Eq. 8 into Eq. 6 gives

$\begin{matrix}{\left. {F_{m}(k)} \right|_{{k = 0},{{1\;\ldots\mspace{11mu} 2^{N}} - 1}} = {\left( {\frac{k}{\Delta_{m}} + {\sum\limits_{n = 0}^{N - 1}\frac{1}{f_{m,n}^{0}}}} \right)^{- 1}.}} & {{Eq}.\mspace{14mu} 9}\end{matrix}$

Further, substituting Eq. 8 into Eq. 9 gives an expanded form for themodule focal length

$\begin{matrix}{F_{m} \in {\left\{ {\left( {\sum\limits_{n = 0}^{N - 1}\frac{1}{f_{m,n}^{0}}} \right)^{- 1},\left( {\frac{1}{\Delta_{m}} + {\sum\limits_{n = 0}^{N - 1}\frac{1}{f_{m,n}^{0}}}} \right)^{- 1},{\left( {\frac{2}{\Delta_{m}} + {\sum\limits_{n = 0}^{N - 1}\frac{1}{f_{m,n}^{0}}}} \right)^{- 1}\mspace{11mu}\ldots\mspace{14mu}\left( {\frac{\left( {2^{N} - 1} \right)}{\Delta_{m}} + {\sum\limits_{n = 0}^{N - 1}\frac{1}{f_{m,n}^{0}}}} \right)^{- 1}}} \right\}.}} & {{Eq}.\mspace{14mu} 10}\end{matrix}$

From Eq. 10 it can be seen that F_(m), the effective module focal lengthfor module m, may consist of a set of 2^(N) unique focal lengths.

In one embodiment, the 0-state focal lengths of all N switchableelements 236 within the same module may be identical. For this casef_(m,n) ⁰ will be constant for all values of n. Therefore, in thecurrent embodiment, the 0-state focal lengths of all N switchableelements 236 may be expressed in the shortened formf_(m,n) ⁰=f_(m) ⁰  Eq. 11where the second subscript, n, has been dropped for simplicity due tothe fact that the 0-state focal length is now independent of the valueof n. Generally, however, as described above, the 0-state focal lengthof the N switchable elements 236 within a module may have any value.

Substituting Eq. 11 into Eqs. 9 and 10 gives simplified forms for F_(m)

$\begin{matrix}{{\left. {F_{m}(k)} \right|_{{k = 0},{{1\;\ldots\; 2^{N}} - 1}} = \left( {\frac{N}{f_{m}^{0}} + \frac{k}{\Delta_{m}}} \right)^{- 1}},} & {{Eq}.\mspace{14mu} 12}\end{matrix}$and in expanded form

$\begin{matrix}{F_{m} \in {\left\{ {\left( \frac{N}{f_{m}^{0}} \right)^{- 1},\left( {\frac{1}{\Delta_{m}} + \frac{N}{f_{m}^{0}}} \right)^{- 1},{\left( {\frac{2}{\Delta_{m}} + \frac{N}{f_{m}^{0}}} \right)^{- 1}\mspace{11mu}\ldots\mspace{14mu}\left( {\frac{\left( {2^{N} - 1} \right)}{\Delta_{m}} + \frac{N}{f_{m}^{0}}} \right)^{- 1}}} \right\}.}} & {{Eq}.\mspace{14mu} 13}\end{matrix}$

A module focal power for module m may be introduced asP _(m) =F _(m) ⁻¹.  Eq. 14

Substituting Eq. 14 into Eqs. 12 and 13 gives

$\begin{matrix}{\left. {P_{m}(k)} \right|_{{k = 0},{{1\;\ldots\mspace{11mu} 2^{N}} - 1}} = {\frac{N}{f_{m}^{0}} + \frac{k}{\Delta_{m}}}} & {{Eq}.\mspace{14mu} 15}\end{matrix}$and in expanded form

$\begin{matrix}{P_{m} \in {\left\{ {\left( \frac{N}{f_{m}^{0}} \right),\left( {\frac{1}{\Delta_{m}} + \frac{N}{f_{m}^{0}}} \right),{\left( {\frac{2}{\Delta_{m}} + \frac{N}{f_{m}^{0}}} \right)\mspace{11mu}\ldots\mspace{14mu}\left( {\frac{\left( {2^{N} - 1} \right)}{\Delta_{m}} + \frac{N}{f_{m}^{0}}} \right)}} \right\}.}} & {{Eq}.\mspace{14mu} 16}\end{matrix}$

From Eqs. 12 and 15 it can be seen that F_(m) and P_(m) (where k hasbeen dropped from both functions for simplicity) are functions of theindexing variable k. It thus follows from these equations, and from Eqs.13 and 16, that the module focal length F_(m), and module focal powerP_(m), of module m are selectable from a set of 2^(N) focal lengths forthe switchable elements. It also follows that each focal length (orfocal power) corresponds to a unique combination of states for the Nswitchable elements in module m. In this sense, module m is capable ofperforming a “quantized zoom” function in that its module focal length(or focal power) may be varied between a number of quantized focallengths (or focal powers). The addition of other optical elements, suchas conventional lenses, in the module will affect the F_(m) and P_(m) ina fashion that will be understood by those skilled in the art.

In another embodiment of the invention the 0-state focal length of eachof the N switchable elements in module an may be fixed at a distance ofinfinity,f_(m) ⁰=∞mm.  Eq. 17

Substituting Eq. 17 into Eqs. 12, 13 and 16 gives the followingexpressions for module focal length and module focal power. For thefocal length,

$\begin{matrix}{{\left. {F_{m}(k)} \right|_{{k = 0},{{1\;\ldots\mspace{11mu} 2^{N}} - 1}} = \frac{\Delta_{m}}{k}},} & {{Eq}.\mspace{14mu} 18}\end{matrix}$and in expanded form

$\begin{matrix}{{F_{m} \in \left\{ {\frac{\Delta_{m}}{0},\frac{\Delta_{m}}{1},{\frac{\Delta_{m}}{2}\mspace{11mu}\ldots\mspace{14mu}\frac{\Delta_{m}}{2^{N} - 1}}} \right\}};} & {{Eq}.\mspace{14mu} 19}\end{matrix}$and, in terms of focal power

$\begin{matrix}{{\left. {P_{m}(k)} \right|_{{k = 0},{{1\;\ldots\mspace{11mu} 2^{N}} - 1}} = \frac{k}{\Delta_{m}}},} & {{Eq}.\mspace{14mu} 20}\end{matrix}$and in expanded form

$\begin{matrix}{P_{m} \in {\left\{ {\left( \frac{0}{\Delta_{m}} \right),\left( \frac{1}{\Delta_{m}} \right),{\left( \frac{2}{\Delta_{m}} \right)\mspace{11mu}\ldots\mspace{14mu}\left( \frac{\left( {2^{N} - 1} \right)}{\Delta_{m}} \right)}} \right\}.}} & {{Eq}.\mspace{14mu} 21}\end{matrix}$

Referring now to FIG. 3, a digital focus lens system according toanother embodiment of the present invention is shown and indicatedgenerally at 700. Lens system 700 includes an optical module 710.Although only a single module 710 is shown in the figure, any number ofmodules may be incorporated in the system 700. Module 710 has an inputface 712 for receiving input light generally indicated by 714 directedinto module 710. Light 714 may coherent or incoherent, and may originatefrom light sources including without limitation, light emitting diodes(LEDs), spatial light modulators, scanners, lasers, light bulbs, naturallighting (for example, sunlight), images (such as those generated bysuch LED or liquid crystal arrays or other optical systems such astelescopes, displays or microscopes). Similarly, module 710 has anoutput face 716 for emitting output light generally indicated at 718which has been transmitted through module 710. Module 710 comprises anoptical element stack 719. Stack 719 includes a number of opticalelements, preferably in generally close proximity and orientation to oneanother such that the standard analytic approximations well known in thefield of optics may apply. Such approximations include withoutlimitation, thin lens and paraxial approximations.

Stack 719 may comprise a first sub-stack 720. First sub-stack 720 maycomprise a number of non-switchable elements 740, 742. While only twonon-switchable elements 740, 742 are shown in FIG. 3, any number ofnon-switchable elements may be incorporated. Preferably, each of thenon-switchable elements 740, 742 comprises a number of optical elementswhich are capable of performing the functions of a thin lens, however,any refractive, diffractive, reflective or other conventional opticalelements for the modulation of phase, frequency and/or amplitude ofelectromagnetic radiation may be employed. For example, non-switchableelements 740, 742 may include without limitation, mirrors, lenses,diffraction gratings, prisms, polarizers, faraday rotators, biaxialcrystals, optical films and coatings, optical gain media, nonlinearoptical materials, spatial filters, wavelength-selective filters,holographic optical elements, or other conventional on-axis or off-axisoptical elements. Preferably, each of the non-switchable elements 740,742 are capable of performing phase modulation functions similar to thatof a lens, and will have a specific F#, optical axis 748, 749, and focallength. Some or all of the focal lengths of non-switchable elements 740,742 may be identical or unique from the others. Preferably, the opticalaxes 748, 749 are collinear. Alternatively, non-switchable elements 740,742 may comprise a single non-switchable element 760.

Lens stack 719 may further comprise a second sub-stack 730. Secondsub-stack 730 may comprise a stack of switchable elements, indicated at750, 752, 754. While only three switchable elements 750, 752, 754 areshown, any number of switchable elements may be incorporated.Preferably, each switchable element 750, 752, 754 comprises a variablefocal length- or switchable-lens, however, any switchable refractive,diffractive, reflective or other optical elements for the modulation ofphase, frequency and/or amplitude of electromagnetic radiation may beemployed. As discussed previously, examples of switchable elementsinclude without limitation liquid crystals (LCs), holographic opticalelements, polymer-dispersed liquid crystals, nonlinear optical lenses,electro-optic elements, electro-optic lenses, LC lenses, LC prisms, LCgratings, LC shutters, LC aperture stops, LC irises, polymer dispersedliquid crystals, switchable holographic optical elements (HOEs),polarization rotators, isotropic, uniaxial, biaxial and/or otheranisotropic optical materials, deformable mirrors and deformablegratings, and micro-electro-mechanical systems (MEMS) and MEMS mirrors.The number of switchable elements 750, 752, 754 and the number ofnon-switchable elements 740, 742 may be identical or different.Preferably, each of the switchable elements 750, 752, 754 are capable ofperforming phase modulation functions similar to that of a number oflenses, and will have specific F#'s, optical axes, and focal lengths.Each of the switchable elements 750, 752, 754 may be switched between atleast a specific first state (“0-state”) and a specific second state(“1-state”).

While only two states (0-state and 1-state) are discussed here for eachof switchable elements 750, 752, 754, any number of states may beemployed. Preferably, for each of the switchable elements 750, 752, 754the 0-state corresponds to a specific first focal length (0-state focallength) having a 0-state optical axis 758, 759, 760 and 0-state F#.Likewise, for each of the switchable elements 750, 752, 754 the 1-statecorresponds to and a specific second focal length (1-state focal length)having a 1-state optical axis 762, 763, 764 and a 1-state F#.Preferably, the 0-state focal lengths for the switchable elements 750,752, 754 are identical and at a distance of infinity. However, any0-state focal lengths may be employed by switchable elements 750, 752,754. Each of the switchable elements 750, 752, 754 will preferably havea specific F#, optical axis 758, and focal length for each of the0-states and 1-states. Preferably, 1-state focal length for each ofswitchable elements 750, 752, 754 will be unique and will follow therelation similar to that described in Eq. 5 above. Preferably, theoptical axes 748, 749, 758, 759, 760, 762, 763, 764 are collinear.Preferably, first sub-stack 720 and second sub-stack 730 are preferablyof nominal thickness and in close contact with one another such thatapproximations, well known in the field of optics, including withoutlimitation the thin-lens-close-contact approximations may apply toelements in both stacks 720, 730. Preferably, switchable elements 750,752, 754 may be activated in any combination of 1-states and 0-statessimultaneously. In this fashion, module 710 may have a module focallength generally corresponding to the inverse of the sum of inversefocal lengths of switchable elements 750, 752, 754. It also follows thatthe module focal length will be selectable from a prescribed set ofpossible values. Preferably, the module focal length will followrelations similar to those described in Eqs. 3, 4, 6, 9, 10, 12, 13, 18and 19 above.

Switchable elements 750, 752, 754 are connected to control cable 770.Control cable 770 connects to controller 772 which provides energy (suchas voltage, current, or charge) and control signals for activating andselecting the states of switchable elements 750, 752, 754. Preferably,each of switchable elements 750, 752, 754 are fabricated and arrangedsuch that each of the 1-state focal lengths serves to focus light 718 ata corresponding focal point which is at a unique distance from outputface 716. When input light 714 is generally collimated, or originatesfrom a light source an approximately infinite distance from input face712, output light 718 will be focused at a point located at a distancefrom output face 716 approximately equal to the module focal length.

The following examples will use the previously discussed notationF_(m)(k) to describe the module focal length; the subscript m indicatesthe module number, and the number “k” in parentheses specifies the indexnumber for the module focal length that has been selected from the setof possible values (see Eqs. 8, 9, 10, 12, 13, 18 and 19, above). Forexample, in the preferred embodiment, when all elements 750, 752, 754are activated in the 0-states, module 710 will have a module focallength F_(m)(0) and the transmitted light may be focused at a point Alocated a generally infinite distance from output face 716 and indicatedby ray 780.

Alternatively, however, system 700 may be configured such that point Ais located at a finite distance from output face 716. When element 750is in the 1-state and elements 752, 754 are in the 0-states, the modulefocal length will correspond to F_(m)(1) and light 718 may be focused ata point B. When element 752 is in the 1-state and elements 750, 754 arein the 0-states, the module focal length will correspond to F_(m)(2) andlight 718 may be focused at a point C. When elements 750, 752 are in the1-states and element 754 is in the 0-state, the module focal length willcorrespond to F_(m)(3) and light 718 may be focused at a point D. Whenelement 754 is in the 1-state, and elements 752, 754 are in the0-states, the module focal length will correspond to F_(m)(4) and light718 may be focused at a point E. When elements 750, 754 are in the1-states and element 752 is in the 0-state, the module focal length willcorrespond to F_(m)(5) and light 718 may be focused at a point F. Whenelements 752, 754 are in the 1-states and element 750 is in the 0-state,the module focal length will correspond to F_(m)(6) and light 718 may befocused at a point G.

Finally, when all elements 750, 752, 754 are activated in the 1-statesand no elements are in the 0-states, the module focal length willcorrespond to F_(m)(7) and light 718 may be focused at a point H.Controller 772 may also provide signals such that any portion ofswitchable elements 750, 752, 754 are activated simultaneously in anycombination of states. In this fashion, elements 750, 752, 754 mayperform any combination of 0-state and 1-state optical functionssimultaneously. Further, the relative portions of light 714, 718 that ismodified by 0-states and 1-states of elements 750, 752, 754 may bedetermined by controller 772. In this fashion, the module 710 maysimultaneously have a plurality of module focal lengths and light 718may be focused simultaneously at combinations of points A, B, C, D, E,F, G, and H. The module focal length can also be expressed in terms of amodule focal power, P_(m)(k), similar to the relationships described inEqs. 14, 15, 16, 20, 21 above.

The module focal power, P_(m)(k), may be selected from a set of valuesthat are determined by the combination of states of elements 750, 752,754. The possible values for P_(m)(k) comprise a sequence of values,similar to the relation described in Eq. 20; in this fashion, the value(or, “state”) of the module focal power is a linear function of thevalue of k. It follows from this that, since k is a value (or “state”)indicating the combination of states of the switchable elements, themodule focal power is thus a function of the combination of states ofthe switchable elements.

Referring now to FIG. 4, a stack of switchable elements according to anembodiment of the present invention is shown and indicated generally at800. Stack 800 includes switchable elements, generally indicated at 750,752, 754. While three elements 750, 752, 754 are shown, any number maybe employed in stack 800. Elements 750, 752, 754 may each include aliquid crystal lens interposed between substrates 832, 834, 836, 838.Substrates 832, 834, 836, 838 are at least partially transparent tolight 820, 830 transmitted through stack 800. Substrates 832, 834, 836,838 may comprise glass, plastic, acrylic resin, polymer, crystal, thinfilms or other materials known to provide a structure for layeredelectro-optic devices. Substrates 832, 834, 836, 838 each have a firstsubstrate surface and a second substrate surface 839 and 840, 842 and844, 846 and 848, 850 and 852, respectively. At least a portion ofsubstrate surfaces 839, 840, 842, 844, 846, 848, 850, 852 can include anantireflection coating as may be desirable for minimizing the loss oflight 820, 830 transmitted through stack 800. At least a portion ofsubstrate surfaces 840, 842, 844, 846, 848, 850 are deposited with agenerally transparent electrical conductors such as indium tin oxide orconducting polymer. Deposited on the conductive substrate surfaces 840,842, 844, 846, 848, 850 are lens function layers 860, 862, 864, 866,868, 870. Lens function layers 860, 862, 864, 866, 868, 870 may consistof materials that may be patterned and include without limitationpolymer, epoxy, polymer-dispersed liquid crystal, poly (methylmethacrylate) (PMMA) or photoresist. Lens function layers 860, 862, 864,866, 868, 870 are at least partially transparent to light 820, 830transmitted through stack 800. A portion of the lens function layers860, 862, 864, 866, 868, 870 also are patterned such that the thickness,index of refraction, transmittance, scattering, absorption or otheroptical property of each layer spatially varies, and, in turn, mayperform a phase, amplitude and/or frequency modifying function on lighttransmitted through the layers. Lens function layers 860, 862, 864, 866,868, 870 may be patterned using techniques that include withoutlimitation as optical lithography, electron-beam lithography, UV lightexposure, holographic, laser or other interferometry, or contact patterntransfer from a patterned substrate to a portion of the lens functionlayers. Preferably, lens function layers 860, 862, 864, 866, 868, 870are patterned with a lens function including without limitation, theoptical properties of lenses such as thin, thick, Fresnel, concave,convex, binary, diffracting, aspheric, on-axis, off-axis, cylindrical,holographic and other lenses. Lens function layers 860, 862, 864, 866,868, 870 may also include alignment grooves or additional alignmentlayers to provide a desired orientation or alignment of liquid crystalmonomers. Lens function layers 860, 862, 864, 866, 868, 870 arepreferably separated by spacers 880, 881, 882, 883, 884, 885. Spacers880, 881, 882, 883, 884, 885 serve to provide cells 890, 892, 894between adjacent pairs of layers 860, 862, 864, 866, 868, 870, and maycomprise such materials as mylar, photoresist, glass fiber, glass orplastic spheres or other films or materials of generally uniform orcontrolled thickness. At least a portion of cells 890, 892, 894 arefilled with liquid crystal fluid 900, 902, 904. Liquid crystal 900, 902,904 may include without limitation one or more of a liquid crystalmaterial, liquid crystal, doped liquid crystal, doped liquid crystalmaterial, a nematic liquid crystal, a nematic liquid crystal material, asmectic liquid crystal, a smectic liquid crystal material, aferroelectric liquid crystal, a ferroelectric liquid crystal material ora polymer dispersed liquid crystal material. Conductor surfaces 840,842, 844, 846, 848, 850 are connected to control cables 910, 912, 914.Control cables 910, 912, 914 are connected to controller 772. Controller772 provides voltage to control cables 910, 912, 914 and provideselectric fields across pairs of conducting surfaces 840, 842, 844, 846,848, 850 which control the molecular orientation of liquid crystal 900,902, 904.

By way of example, switchable elements 750, 752, 754 may be configuredsimilar to conventional nematic liquid crystal cells having parallelhomogeneous alignment. Considering element 750 when no electric field isapplied across conducting surfaces 840, 842, molecules of liquid crystal900 are aligned such there exists a first refractive-index mismatchbetween liquid crystal 900 and layers 860, 862. This firstrefractive-index mismatch results in element 750 having a first focallength (0-state focal length) for light 820 of a specific polarization.In the presence of an electric field across conducting surfaces 840,842, molecules of liquid crystal 900 are aligned such there exists asecond refractive-index mismatch between liquid crystal 900 and layers860, 862. This second refractive-index mismatch results in element 750having a second focal length (1-state focal length) for light 820 of aspecific polarization. Similarly, element 752 will have a 0-state focallength with no electric field applied across conducting surfaces 844,846, and will have a 1-state focal length in the presence of an electricfield. Likewise, element 754 will have a 0-state focal length with noelectric field applied across conducting surfaces 848, 850, and willhave a 1-state focal length in the presence of an electric field.Additional swtichable elements 920 may be included in stack 800.Alternately, the 0-state and 1-state focal lengths may correspond to thepresence and absence of electric fields, respectively. The relationshipbetween the state of focal length and the absence, or presence, of theapplied electric field may depend on factors including withoutlimitation, orientation of alignment grooves, types of liquid crystal,refractive indexes of lens function layers, the amplitude, frequency anddirection of displacement fields in the liquid crystal, amplitude andfrequency of applied electric fields and voltage potentials across thecells and the polarization of light 820. Additional elements 920 mayinclude without limitation liquid crystal lenses similar to thosedescribed above, polarizers, liquid crystal- or other-variable aperturesor field stops, tunable color filters, variable polarization rotatorsand retarders, deformable mirrors and MEMS devices. Further, additionalnon-switchable elements 760 may be included in stack 800. Preferably,0-state focal lengths of each of elements 750, 752, 754 will beapproximately infinity; this may be accomplished, for example, when thelens function layers 860, 862, 864, 866, 868, 870 are generallyindex-matched to the extra-ordinary index of the corresponding liquidcrystal 900, 902, 904. Alternatively, switchable elements 750, 752, 754may be configured similar to other liquid crystal configurations,including without limitation twisted or super-twisted nematic liquidcrystal cells whereby the focusing properties of the switchable lensesare generally independent of the polarization of the light 820.

Preferably, 1-state focal lengths of each of elements 750, 752, 754 willfollow relationships similar to the 2″ relationships described in Eq. 5above. For example, the 0-state focal lengths of elements 750, 752, 754may all be infinite. However, elements 750, 752, 754 may have 1-statefocal lengths with values of

$\frac{\Delta_{m}}{2^{0}},{\frac{\Delta_{m}}{2^{1}}\mspace{14mu}{and}\mspace{14mu}\frac{\Delta_{m}}{2^{2}}},$respectively, where Δ_(m) is a constant having the dimension of length.It follows that, in the present example, Δ_(m) may be equal to the1-state focal length of element 750 (f_(m,0) ¹). In this fashion,elements 750, 752, 754 may have 1-state focal lengths of f_(m,0) ¹,

$\frac{f_{m,0}^{1}}{2},\frac{f_{m,0}^{1}}{4},$respectively.

Turning now to FIG. 5, an alternative embodiment of the stack ofswitchable elements is shown and generally indicated at 1000. The samecomponents as in FIG. 4 have the same assigned number as in FIG. 4.Stack 1000 includes a plurality of switchable elements, indicatedgenerally at 750, 752, 754. A first transparent substrate 832 has afirst conductive surface 840 that is at least partially coated with anoptically transparent, electrically conductive layer such as indium tinoxide. Conductive surface 840 is at least partially deposited with afirst lens function layer 860. First lens function layer 860 may have anumber of optical phase- and/or amplitude-modifying functions embeddedin it. Additionally, first lens function layer 860 may have alignmentgrooves or features for providing liquid crystal monomer alignment.First spacers 880, 881 are deposited on first lens function layer 860and have a controlled thickness. Second lens function layer 862 isdeposited on spacers 880, 881 thereby forming a first cell 890. Secondlens function layer 862 may also have a number of optical phase- and/oramplitude-modifying functions imbedded in it. Second lens function layer862 is deposited on a second conductive surface 1180. Second conductivesurface 1180 is deposited on a first transparent film 1100. Firsttransparent film 1100 may be comprised of optically transparentmaterials including without limitation glass, vinyl-acetate, thin coatsputtered- or evaporated-films, plastic or polymer. First transparentfilm 1100 may include an optical phase- and/or amplitude-modifyingfunction, such as a lens function, imbedded in it. A third lens functionlayer 864 is deposited on first transparent film 1100. Third lensfunction layer 864 may include a number of optical phase- and/oramplitude-modifying functions imbedded in it. Second spacers 882, 883are deposited on third polymer layer 864.

A fourth lens function layer 866 is deposited on second spacers 882, 883thereby forming a second cell 892. Fourth lens function layer 866 mayinclude a number of optical phase- and/or amplitude-modifying functions.Fourth lens function layer 866 is deposited on a third conductivesurface 1182. Third conductive surface 1182 is deposited on a secondtransparent film 1102. Second transparent film 1102 may be comprised ofoptically transparent materials including without limitation glass,vinyl-acetate, plastic or polymer. Second transparent film 1102 mayinclude an optical phase modifying function imbedded in it. A fifth lensfunction layer 868 is deposited on second transparent film 1102. Fifthlens function layer 868 may include a number of optical phase- and/oramplitude-modifying functions. Third spacers 884, 885 are deposited onfifth polymer layer 868. A sixth lens function layer 870 is deposited onthird spacers 884, 885 thereby forming a third cell 894. Sixth lensfunction layer 870 may include a number of optical phase- and/oramplitude-modifying functions imbedded in it. Sixth polymer layer 870 isdeposited on a fourth conductive surface 1184. Fourth conductive surface1184 is deposited on a second transparent substrate 1200. Liquid crystalmaterial 1206, 1207, 1208 is deposited in cells 890, 892, 894,respectively. Liquid crystal may include one or more of a liquid crystalmaterial, liquid crystal, doped liquid crystal, doped liquid crystalmaterial, a nematic liquid crystal, a nematic liquid crystal material, asmectic liquid crystal, a smectic liquid crystal material, aferroelectric liquid crystal, or a ferroelectric liquid crystalmaterial.

Conductor surfaces 840, 1180, 1182, 1184 are connected to control cablesindicated generally at 1210. Control cables 1210 are connected tocontroller 1220. Second conducting surface 1180 functions as a commonelectrode to switchable elements 750 and 752. Likewise, third conductingsurface 1182 functions as a common electrode to switchable elements 752and 754. Controller 1220 provides voltages to control cables 1210 suchthat electric fields formed across elements 750, 752, 754 are ofappropriate modulation, amplitude and sign such that the liquid crystalmonomers in cells 890, 892, 894, become aligned to desired orientations.In this fashion, switchable elements 750, 752, 754 function asindependently switchable lenses. Also, in this fashion, any number ofsimilar switchable elements may be incorporated in stack 1000.

Preferably the thickness of the optical components in between firstsubstrate 832 and second substrate 1200 is of appropriate thickness,relative to parameters such as the numerical apertures of the lensfunctions of switchable elements, and the wavelengths of lighttransmitted through stack 1000, such that the thin-lens-close-contactapproximations, known in the field of geometric optics, can be applied.For example, with no electric field applied across conducting surfaces1180, 1182 and no electric field applied across surfaces 1182, 1184,switchable elements 752, 754 are in the 0-states, and hence may functionas lenses having infinite focal lengths. With the proper electric fieldapplied across conducting surfaces 840, 1180, switchable element 750 isswitched to the 1-state, and hence may function as a lens having afinite focal length, of, for example, f_(m,0) ¹. In this fashion, light1210 emitted from light source 1238, and is transmitted through stack1000, will be focused at a point B. Under these same conditions, butwith an electric field now also applied across conducting surfaces 1182,1184, liquid crystal monomers 1230 become aligned such that switchableelement 754 is switched to the 1-state, and hence may function as a lenshaving a finite focal length, of, for example,

$\frac{f_{m,0}^{1}}{4}.$In this fashion, for example, light input light indicated at 1239 isemitted from light source 1238. Input light 1239 is transmitted throughstack 1000 and is transmitted as light generally indicated as 1250. Inthis fashion transmitted light 1250 may therefore be redirected byswitchable elements 750, 754, and may be focused at a point F.Generally, in this fashion, for the various combinations of states forthe three switchable elements 750, 752, 754, given in this example,transmitted light 1250 may be focused at focal points indicated at A, B,C, D, E, F, G, and H.

Alternatively, some or all of switchable elements 750, 752, 754 may beconfigured such that, with appropriate applied voltages, the focallengths may be continuously tunable instead of being selectable for adiscrete set of focal lengths. For example, such continuously tunableconfigurations may include without limitation nematic liquid crystalcells in parallel homogeneous alignment and electro-optic lenses.

Alternatively, focal points A, B, C, D, E, F, G, and H may comprisefocal planes whereby the transmitted light 1250 forms a virtual or realimage at focal planes A, B, C, D, E, F, G, and H. While only threeswitchable elements 750, 752, 754 are described here, any number of Nswitchable elements may be incorporated in embodiments of the presentinvention. In this fashion, the number of selectable focal points mayincrease proportionally with the function 2^(N).

Turning now to FIG. 6, an alternative embodiment of the stack ofswitchable elements is shown and generally indicated at 1000′. The samecomponents as in FIG. 5 have the same assigned number as in FIG. 5.Stack 1000 includes a plurality of switchable elements, indicatedgenerally at 750, 752, 754. A first transparent substrate (firstsubstrate) 832 has a first optically transparent, electricallyconductive surface 840. First conductive surface 840 is at leastpartially deposited with a first lens function layer 860. First lensfunction layer 860 has an optical phase- and/or amplitude-modifyingfunction, such as a lens, prism, grating, or other optical function,imbedded in it and may include without limitation materials suchpolymer, epoxy, PMMA and photoresist.

First spacers 880, 881 are deposited on lens function layer 860 and havea controlled thickness. A second lens function layer 862 is deposited onspacers 880, 881 thereby forming a first cell 890. Second lens functionlayer 862 is deposited on a first electrically conductive substrate1410. First electrically conductive substrate (first conductivesubstrate) 1410 provides both electrical conductivity and structuralsupport to element 750 and to stack 1400 in general. A third lensfunction layer 864 is deposited on first conductive substrate 1410.Second spacers 882, 883 are deposited on third lens function layer 864.

A fourth lens function layer 866 is deposited on second spacers 882, 883thereby forming a second cell 892. Fourth lens function layer 866 isdeposited on a second electrically conductive substrate 1420. Secondelectrically conductive substrate (second conductive substrate) 1420provides both electrical conductivity and structural support to element752 and to stack 1400 in general. A fifth lens function layer 868 isdeposited on second conductive substrate 1420. Third spacers 884, 885are deposited on fifth layer 868. A sixth lens function layer 870 isdeposited on third spacers 884, 885 thereby forming a third cell 894.Sixth lens function layer 870 is deposited on a second conductivesurface 1184. Fourth conductive surface 1184 may be deposited on asecond transparent substrate (second substrate) 1200. Generally, in asimilar fashion, first substrate 832 may be at least partiallyelectrically conductive, such that first substrate 832 and firstconductive surface 840 may be combined into a single substrate (notshown). Likewise, second substrate 1200 may be at least partiallyelectrically conductive, such that second substrate 1200 and secondconductive surface 1184 may be combined into a single substrate (notshown). Liquid crystal material 1206, 1207, 1208 is deposited in cells890, 892, 894, respectively. Conductive surfaces (and conductivesubstrates) 840, 1410, 1420, 1184 are connected to control cablesindicated generally at 1210. Control cables 1210 are connected tocontroller 1220. Alternatively, a portion of lens function layers 860,862, 864, 866, 868, 870 may include a partially conductive surface (notshown) or may be coated with a conducting film (not shown) such that theconducting surface or film is in near contact with a portion of theliquid crystal material 1206, 1207, 1208. Additionally, a portion oflens function layers 860, 862, 864, 866, 868, 870 may have alignmentgrooves, coatings or features for providing liquid crystal monomeralignment.

Turning now to FIGS. 7 a– 7 d, a die-stamping replication method forfabricating the portions of the switchable elements, specifically, thelayered structure that includes a substrate, a conductive layer and alens function layer. The same components as in FIG. 4 have the sameassigned number as in FIG. 4. As shown in FIG. 7 a, a transparentsubstrate 832 has a first substrate surface 1305. First substratesurface 1305 has deposited on it an optically transparent, electricallyconductive surface (or, conductive layer) 840 such as ITO.

Conductive layer 840 may be deposited by sputtering or by other knowntechniques. Deposited on conductive layer 840 is a lens function layer860. Lens function layer 860 may include patternable materials includingwithout limitation polymer, epoxy, photoresist or PMMA. Lens functionlayer 860 may be spin-coated on conductive layer 840. Lens functionlayer 860 may deposited in such a fashion as to have a generally uniformthickness, yet will be soft or viscous for a period of time before it ishardened by baking, exposure to ultraviolet (UV) light or otherhardening processes. A die substrate 1300, is comprised of substratematerial that is capable of being patterned or micromachined, includingwithout limitation, glass, plastic, silicon or other substratematerials. Die substrate 1300 has a first die surface 1310. First diesurface 1310 is has a spatially-varying thickness pattern 1320. Whilelens function layer 860 is in its soft or viscous state, die substrate1300 is brought toward it, indicated schematically by an arrow 1330.

Now referring to FIG. 7 b, die substrate 1300 is brought into contactwith lens function layer 860. In this fashion, first die surface 1310 isstamped (FIG. 7 b) onto phase modifying layer 860 so as to transfer aninverse-copy of spatially-varying thickness pattern 1320 into lensfunction layer 860. A release agent (not shown), such a silicone spray,may be deposited on one or more of the first die surface 1310 and thelens function layer 860. The release agent may serve to assist inrelease the of the die substrate 1300 from the lens function layer 860in later steps of the process. This arrangement is then subjected to ahardening force 1340, such as heat that emanates from a heat source (notshown), or from UV light emanating from a UV source (not shown).Hardening force 1340 serves to harden the lens function layer 860. Nowreferring to FIG. 7 c, after lens function layer 860 has beensufficiently hardened, die substrate 1300 (not shown) is removed. Lensfunction layer 860 will now have stamped into it an inverse-copy ofspatially-varying thickness pattern 1350. With appropriate die, lensfunction layer 860 can perform phase-modifying functions such as lensfunctions and other functions including refraction, diffraction,reflection and scattering. Now turning to FIG. 7 d, this method can begenerally repeated using a second substrate surface 1306 of substrate832, or using a plurality of substrates (not shown). In this fashion, asecond lens function layer 1360, or a plurality of lens function layers(not shown) can be patterned, each its own specific phase- and/oramplitude-modifying properties.

Referring now to FIG. 8, a method for controlling the states of theswitchable elements of embodiments of the present invention is shown andgenerally indicated at 1500. The same components as in FIG. 3 have thesame assigned number as in FIG. 3. A signal, generally indicated at S,is generated and provided to controller 772. Signal S containsinformation for controlling the states of switchable elements 750, 752,754. Signal S may be either generated either internally or externally tocontroller 772. A portion of signal S includes a serial data streamcomprising a control word, indicated generally at 1520. Control word1520 is digital word having a bit field length of N bits where N may bea number equal to the number of switchable elements 750, 752, 754 instack 716.

In the current example (FIG. 8), control word 1520 may comprise a 3-bitfield length where the bits are generally indicated at A, B, C, and hasthe base-two value “101”. However, in general, control word 1520 canhave any bit field length and may be comprised of any number of groupsof bits. A demultiplexer 1530 serves to demultiplex control word 1520whereby each of bits A, B. C are routed to a separate port, indicatedgenerally at A′, B′, C′. Each port A′, B′, C′ is connected to additionalelectronics (not shown) including a voltage source (not shown) that are,in turn, connected to a separate switchable element 750, 752, 754. Inthis fashion, bit A provides a signal for controlling the state ofswitchable element 750, bit B provides a signal for controlling thestate of switchable element 752, and bit C provides a signal forcontrolling the state of switchable element 754. Thus, control word1520, serves to control the states (or the, “combination of states”) ofthe switchable elements 750, 752, 754. As was described in FIG. 3, themodule focal power (or the state thereof) is a function of thecombination of states of the switchable elements. Therefore, the stateof the module focal power is a function of the value of control word1520.

Digital Telescope Lens System.

Referring now to FIG. 9, the digital focus lens system is applied to atwo-lens telescope system. It will be seen that the present embodimentof the invention similar to a simple Galilean telescope having digitallyvariable focal length, or zoom, properties. A digital zoom lens system(system) 400 incorporates a first module 410 having a first focallength, F₁ 420. System 400 further incorporates a second module 430having a second focal length, F₂ 440. Second module 430 is located afirst distance, d₁ 450, from first module 410. One or more of the firstmodule 410 and second module 430 may incorporate a number of opticalelements (elements) 460, 464. One or more of elements 460 may includeswitchable elements 470, 474 and may be activated into a number ofstates. The optical axes, generally indicated at 480, of first module410, second module 430, and elements 460, 470, 474, 464 may be generallycollinear. Alternatively, the optical axes of first module 410, secondmodule 430, and elements 460, 470, 474, 464 may be arranged at anyrelative orientations. In the present embodiment, one or more ofelements 470 are similar to thin lenses in close proximity or in contactwith one another, and the thin lens and/or the paraxial approximationsmay apply to portions of first module 410 and/or second module 430.

A first object 490 and a first image 500 are located at distances s_(o1)510 and s_(i1) 520, respectively, from first module 410. Likewise, asecond object 530 and second image 540, are located at distances s_(o2)550 and s_(i2) 560, respectively, from second module 430. Using thestandard lensmakers formula, s_(i1) 520 and s_(i2) 560 can be expressedas

$\begin{matrix}{s_{o1} = \left( {\frac{1}{F_{1}} - \frac{1}{s_{i1}}} \right)^{- 1}} & {{Eq}.\mspace{14mu} 22} \\{and} & \; \\{s_{o2} = \left( {\frac{1}{F_{2}} - \frac{1}{s_{i2}}} \right)^{- 1}} & {{Eq}.\mspace{14mu} 23}\end{matrix}$

Using the definition of s_(o2) 550 similar to that conventionally usedin simple two-lens systemss _(i1) ≡d ₁ −s _(o2),  Eq. 24s_(o1) 510 can be expressed in a form similar to that of common two-lenssystems

$\begin{matrix}{s_{o1} = {\frac{F_{1}\left\lbrack {{s_{i2}\left( {d_{1} - F_{2}} \right)} - {d_{1}F_{2}}} \right\rbrack}{{s_{i2}\left( {d_{1} - F_{1} - F_{2}} \right)} + {F_{2}\left( {F_{1} - d_{1}} \right)}}.}} & {{Eq}.\mspace{14mu} 25}\end{matrix}$

A parameter of system 400, the magnification, M, (or, transversemagnification, M_(T)), is similar to the magnification of a simpletwo-lens system, i.e.,

$\begin{matrix}{{M \equiv M_{T}} = {\frac{- s_{i1}}{s_{o1}} \cdot {\frac{- s_{i2}}{s_{o2}}.}}} & {{Eq}.\mspace{14mu} 26}\end{matrix}$

Substituting for s_(i1) 520 and s_(o2) 550, M can now be expressed as

$\begin{matrix}{{M = \frac{F_{2}F_{1}}{{s_{o1}\left( {d_{1} - F_{1} - F_{1}} \right)} + {F_{1}\left( {F_{2} - d_{1}} \right)}}},} & {{Eq}.\mspace{14mu} 27}\end{matrix}$again, similar to the transverse magnification for standard two-lenssystems.

Now, for a zoom lens system such as a telescope or telephoto lens, itmay be desirable for s_(i2) 560 to be a generally fixed distance fromsecond module 430 while s_(o1) 510 is variable over a specified range ofdistances from first module 410. In this fashion, a system focal length570, given as the distance between s_(o1) 510 and s_(i2) 560, is avariable. However, it is often difficult to construct such a system inwhich M, s_(i2) 560 and d₁ 450 are all constant while s_(o1) 510 isvariable. In a present embodiment of the invention, a telescope based oncombinatorial optics is enabled in which M, s_(i2) 560 and d₁ 450 areconstant while s_(o1) 510 is variable.

To accomplish this, for example, F₁ 420 may be constant and F₂ 440 mayhe variable and expressed as a function of k, i.e., F₂(k), and given aform similar to that described in Eq. 12,

$\begin{matrix}{{\left. {F_{2}(k)} \right|_{{k = 0},{{1\;\ldots\mspace{11mu} 2^{N}} - 1}} = \left( {\frac{N}{f_{2}^{0}} + \frac{k}{\Delta_{m}}} \right)^{- 1}},} & {{Eq}.\mspace{14mu} 28}\end{matrix}$where, for this example, the 0-states of the N switchable elements 474of the second module 430 are identical. Substituting Eq. 28 into Eq. 27gives an expression for M as a function of the variable k, i.e., M(k),

$\begin{matrix}{\left. {M(k)} \right|_{{k = 0},{{1\;\ldots\mspace{11mu} 2^{N}} - 1}} = {{\left( {{- \frac{N}{f_{2}^{0}}} - \frac{k}{\Delta_{m}} + {\left( {\frac{d_{1}N}{f_{2}^{0}} - \frac{{f_{2}^{0}\Delta_{m}} - {d_{1}{kf}_{2}^{0}}}{f_{2}^{0}\Delta_{m}}} \right)\frac{1}{F_{1}}}} \right)s_{i2}} + 1 - {\frac{d_{1}}{F_{1}}.}}} & {{Eq}.\mspace{14mu} 29}\end{matrix}$

Setting the first derivative of M(k) with respect to k equal to 0, i.e.,

$\begin{matrix}{\frac{\partial{M(k)}}{\partial k} = 0} & {{Eq}.\mspace{14mu} 30}\end{matrix}$a solution is found for F₁ 420F₁=d₁.  Eq. 31

Substituting Eqs. 31 and 28 into Eq. 25 gives

$\begin{matrix}{s_{{o1}{(k)}} = {{\left( {\frac{- k}{\Delta_{m}} + \frac{1}{s_{i2}} - \frac{N}{f_{2}^{0}}} \right)d_{1}^{2}} + {d_{1}.}}} & {{Eq}.\mspace{14mu} 32}\end{matrix}$

Substituting Eq. 31 into Eq. 29, gives and M as constant,

$\begin{matrix}{M = {- {\frac{s_{i2}}{d_{1}}.}}} & {{Eq}.\mspace{14mu} 33}\end{matrix}$

An object separation constant, δs_(o1) 580, having the dimension oflength, can be defined as the derivative of s_(o1) 510 with respect tok, i.e.,

$\begin{matrix}{{{\delta\; s_{o1}} \equiv \frac{\partial s_{{o1}{(k)}}}{\partial k}} = {- {\frac{d_{1}^{2}}{\Delta_{m}}.}}} & {{Eq}.\mspace{14mu} 34}\end{matrix}$

An initial object plane s_(o1(0)) 590, i.e., the value of s_(o1(k)) fork=0, can be expressed as

$\begin{matrix}{s_{{o1}{(0)}} = {d_{1} - \frac{N\; d_{1}^{2}}{f_{2}^{0}} + {\frac{d_{1}^{2}}{s_{i\; 2}}.}}} & {{Eq}.\mspace{14mu} 35}\end{matrix}$

Substituting Eqs. 34 and 35 into Eq. 32 gives

$\begin{matrix}{{{s_{o1}(k)}❘_{{k = 0},{{1\mspace{11mu}\ldots\mspace{11mu} 2^{N}} - 1}}} = {s_{{o1}{(0)}} + {\delta\; s_{o1}{k.}}}} & {{Eq}.\mspace{14mu} 36}\end{matrix}$and in expanded forms_(o1)ε{(s_(o1(0))),(s_(o1(0)+δs) _(o1)) . . . (s_(o1(0)+δs)_(o1)└2^(N)−1┘)}.  Eq. 37

From the above discussion, it can be seen that the present embodiment ofthe invention is similar to a telescope with quantized or “digital” zoomcontrol of the focal length. In particular, system 400 is similar to aGalilean telescope, wherein: F₁ 420 and F₂ 440 are similar to the fieldlens and ocular lens, respectively; wherein d₁ 450 is similar to thedistance separating F₁ 420 and F₂ 440; and wherein M, s_(o1) 510 ands_(i2) 560 are similar to the transverse magnification, object distanceand image distance, respectively. However, the present embodiment of theinvention has the following distinctive properties: s_(o1) 510 isselectable from a set of quantized locations relative to the location ofF₁ 420; the relative locations of F₁ 420 and F₂ 440 may be fixed suchthat d₁ 450 may have a constant value for all object distances in theset of s_(o1) s_(i2) 560 and M may both have constant values for allobject distances in the set of s_(o1) and the system and its componentsmay be solid state, i.e., comprise no moving parts.

Digital Camera Lens System.

In cases where s_(i2) has a negative value, the image formed by thesystem is a virtual image and the system can function similarly tosimple two-lens telescope. In this fashion, remote objects may beviewable by the human eye and may not require additional opticalelements for viewing such as oculars. However, when s_(i2) has apositive value, the image formed by the system is a real image and thesystem may function as an imaging system such as a camera. For example,the system may function as a camera wherein an image sensor (sensor) maybe positioned a distance s_(i2) from F₂. Such sensors may include,without limitation, CCD arrays, CMOS image sensors or sensor arrays,artificial retinas or conventional photographic film. In this fashion,information, pertaining to the image of a object located at a distanceso, from F₁, may be captured by the sensor.

Additional optical elements may be in incorporated in all embodiments ofthe invention in fashions similar to those used commonly in telescopes,cameras and other imaging and non-imaging systems or in other ways thatwill be understood by those skilled in the art. Examples of suchadditional optical elements may include without limitation oculars,field lenses, and apertures, stops, partially- or fully-reflectivemirrors, prisms, gratings, lenses, and lens complexes.

Digital Projector Lens System.

In another embodiment of the present invention, the system may beconfigured to function as an image projector. For example, with 2-lensimage projectors, generally, an object is located at a distance, s_(o1)from an object lens, L₁; an image is formed at a distance, s_(i2), froman image lens L₂; and L₁ and L₂ are separated by a distance d₁.Similarly to telescopes, for image projectors it is sometimes desirablefor both the-separation distance between the two optical elements d₁ andthe magnification M to have constant values. In the previous preferredembodiment of a digital telescope lens system, s_(i2) was held constantwhile s_(o1) was variable. However, for the present embodiment of adigital projector lens system, it may be desirable that s_(i2), bevariable while s_(o1) is held constant. To accomplish thisfunctionality, the previous embodiment of the invention is utilized,however, the system may now be flipped relative to the positions of theobject and the image. In this fashion, the F₂, may be left constant andF₁, may now be variable and expressed as a function of the variable k,and given a form similar to that described above and in Eq. 12.

Digital Microscope Lens System.

The above discussions described embodiments of the invention thatutilize digital focus lens systems for purposes that include thecontrolling of the position of an image without requiring changes in themagnification of the image, and while simultaneously allowing the systemto be solid state. Similarly, however, it may also sometimes bedesirable for the system to exhibit properties such as allowing thecontrol of the magnification of an image without requiring changes inthe location of the image, and while simultaneously allowing the systemto be solid state.

For example, for microscopes in general, and specifically for 3-lensmicroscopes, an object may be located at a distance, s_(o1), from afirst module. A second module may be located at a first distance d₁,from the first module. A third module may be located at a seconddistance d₂ from the second module. An image may then be formed at animage distance s_(i3) from the third module. In the present embodimentof a 3-lens microscope, it may be desirable for d₁, d₂, s_(o1) ands_(i3) to all have generally constant values, while it may also bedesirable that the magnification, M, may be variable.

In the previous embodiments, M and d_(l) were held constant while eithers_(o1) or s_(i2) were variable. However, for the present embodiment of acombinatorial optical microscope, the magnification M will now bevariable while s_(o1), s_(i3), d₁ and d₂, will be held generallyconstant. One way to accomplish this functionality incorporates theprevious embodiment of the invention, a digital projector lens systemand a third module having variable focal power. As in the previousembodiment, the focal length of the second module F₂ may be leftconstant. Further, the first module may incorporate switchable elementsas previously described. In this fashion the focal length of the firstmodule F₁, may be variable and expressed as a function of k, and giventhe form similar to that described in Eq. 12.

A solution may be found for which the first derivative of s_(i3) withrespect to k is equal to zero, i.e.,

$\frac{\partial s_{i\; 3}}{\partial\; k} = 0.$

In this fashion, the distance of the image to the third module will be aconstant and independent of the state of variable k. One possiblesolution to the above condition exists for the case when the focal powerof at least one of the modules is continuously variable between twospecified values of focal power. The magnification, M, (or, transversemagnification, M_(T)) of this three-module system may also be similar tothe magnification of a common three-lens system, similar to the previousdiscussion of M for a two-module system,

${M \equiv M_{T}} = {\frac{- s_{i1}}{s_{01}} \cdot \frac{- s_{i2}}{s_{o2}} \cdot {\frac{- s_{i3}}{s_{o3}}.}}$

The desired functionality of M being a variable function of k, M(k), canbe achieved for a system utilizing a module, for example, the thirdmodule, the focal length, F₃, of which is a variable function of k. Waysto achieve this functionality include without limitation the use ofelectro-optic or liquid crystal lenses or other variable or switchableoptical elements that have generally continuously variable focal power.For example, for a material having an r₃₃ or other electro-opticcoefficient, such as lithium niobate, may be polished in the form of alens. Transparent electrodes, such as indium tin oxide, may be depositedon the surfaces of the lens. An electric field may then be applied fromone electrode to the other, across the thickness of the lens. Due to theelectro-optic coefficient of the material of the lens, the index of thelens will be a function of the strength of the applied electric field.In this fashion, the focal length of the lens will also be a function ofthe applied electric field. Similarly, liquid crystal (LC) lenses andgratings, such as modal LCs and LC lenses similar to LC blazed-gratingbeam deflectors based on nematic LC cells in parallel homogeneousalignment can provide variable focusing of the above form.

It will be understood by those skilled in the art of optics that manyadditional optical elements, components, complexes, etc., may beincluded in the present invention; those additional elements have beenomitted from this discussion for simplicity.

While the above is a complete description of the preferred embodiment ofthe present invention, it is possible to use various alternatives,modifications and equivalents. Therefore, the scope of the presentinvention should be determined not with reference to the abovedescription but should, instead, be determined with reference to theappended claims, along with their full scope of equivalents. Theappended claims are not to be interpreted as includingmeans-plus-function limitations, unless such a limitation is explicitlyrecited in a given claim using the phrase “means for.”

1. A Digital Focus Lens System for providing an optical system having aplurality of selectable focal powers, comprising: a first switchableelement capable of being switched between a first-element first-stateand a first-element second-state; and and a second switchable elementcapable of being switched between a second-element first-state and asecond-element second-state; wherein the first switchable element has afocal length f_(m) ⁰ in the first-element first state and the secondswitchable element has the same focal length f_(m) ⁰ in thesecond-element first state, wherein the first and second switchableelements are in optical communication with each other such that each ofthem may contribute to a cumulative focal power, wherein, a first focalpower may be selected by activation of the first switchable element tothe first-element first-state and activation of the second switchableelement to the second-element first-state, wherein a second focal poweris selected by activation of the first switchable element to thefirst-element second-state and activation of the second switchableelement to the second-element first-state, wherein a third focal poweris selected by activation of the first switchable element to thefirst-element first-state and activation of the second switchableelement to the second-element second-state, and wherein a fourth focalpower is selected by activation of the first switchable element to thefirst-element second-state and activation of the second switchableelement to the second-element second-states, wherein the first andsecond switchable elements are two of N switchable elements in a moduleof a device having one or more modules, where N is greater than or equalto two, wherein each of the N switchable elements is independentlyswitchable between discrete first and second states, wherein in thefirst states the focal lengths are the same for all N switchableelements, and wherein in their second states, the focal lengths of the Nswitchable elements are unique and, except for a smallest second statefocal length, each second state focal length is twice as large asanother second state focal length.
 2. The system according to claim 1wherein a portion of the switchable elements include liquid crystallenses.
 3. The system according to claim 1 wherein a portion of theswitchable elements include switchable holographic optical elements. 4.The system according to claim 1 wherein a portion of the switchableelements include polymer dispersed liquid crystal.
 5. The systemaccording to claim 1 wherein a portion of the switchable elements form astack of thin lenses.
 6. The system according to claim 1 furthercomprising one or more non-switchable elements for further modifying theoptical properties of the system.
 7. The system according to claim 1further comprising any number of additional switchable elements.
 8. Thesystem according to claim 1 wherein a portion of the switchable elementsinclude electro-optic lenses.
 9. The system according to claim 1 whereina portion of the switchable elements include liquid crystal and polymerlenses.
 10. The system of claim 1 wherein the digital focus lens systemis a digital telescope, telephoto lens, or zoom lens.
 11. The system ofclaim 1 wherein the digital focus lens system is a digital camera. 12.The system of claim 1 wherein the digital focus lens system is a digitalprojector.
 13. The system of claim 1 wherein the digital focus lenssystem is a digital microscope.
 14. The system of claim 1 furthercomprising a controller for providing control signals that serve toactivate the first and second switchable elements.
 15. The systemaccording to claim 1 wherein a portion of the switchable elements may becontinuously tuned between the focal powers of their respective first-and second- states.
 16. The system of claim 1 further comprising one ormore light sources for providing light to be transmitted through andmodified by the system.
 17. The system of claim 16 wherein the light isreceived and transmitted by the first and second switchable elements andis modified in accordance with the selected focal powers of the firstand second switchable elements.
 18. The system of claim 17 wherein aportion of the light transmitted by the system forms one or more images.19. A method for controlling a digital lens system having N switchableelements in optical communication with each other such that each of themmay contribute to a cumulative focal power, where N is 2 or more,wherein each switchable element is capable of being switched between adiscrete first-state and a discrete second-state, the method comprising:generating a control signal containing information for controlling thestates of each of the N switchable elements; and coupling the controlsignal to the N switchable elements to set the state of each of the Nswitchable elements, and wherein a portion of the control signalincludes a data stream comprising a control word, wherein in the firststates the focal lengths are the same for all N switchable elements, andwherein in their second states, the focal lengths of the N switchableelements are unique and, except for a smallest second state focallength, each second state focal length is twice as large as anothersecond state focal length.
 20. The method of claim 19 wherein thecontrol word is a digital word having a bit field length of N bits. 21.The method of claim 19 wherein the control signal is an electricalsignal.
 22. The method of claim 21 wherein the control signal is at avoltage, current or frequency appropriate for activating the switchableelements to their desired states.
 23. The system of claim 1 wherein oneor more of the first and second switchable elements has a focal powerthat is continuously tunable.
 24. The system of claim 1 wherein one ormore of the first and second switchable elements includes a fluid.
 25. ADigital Focus Lens System for providing an optical system having aplurality of selectable focal powers, comprising: a first switchableelement capable of being switched between a first-element first-stateand a first-element second-state; and and a second switchable elementcapable of being switched between a second-element first-state and asecond-element second-state; wherein the first switchable element has afocal length f_(m) ⁰ in the first-element first state and the secondswitchable element has the same focal length f_(m) ⁰ in thesecond-element first state, wherein the first and second switchableelements are in optical communication with each other such that each ofthem may contribute to a cumulative focal power, wherein, a first focalpower may be selected by activation of the first switchable element tothe first-element first-state and activation of the second switchableelement to the second-element first-state, wherein a second focal poweris selected by activation of the first switchable element to thefirst-element second-state and activation of the second switchableelement to the second-element first-state, wherein a third focal poweris selected by activation of the first switchable element to thefirst-element first-state and activation of the second switchableelement to the second-element second-state, and wherein a fourth focalpower is selected by activation of the first switchable element to thefirst-element second-state and activation of the second switchableelement to the second-element second-state, wherein the first and secondswitchable elements are two of N switchable elements in a module of adevice having one or more modules, where N is greater than or equal totwo, wherein each of the N switchable elements is independentlyswitchable between discrete first and second states, wherein the Nswitchable elements are configured such that a focal length of thesystem can be selected from a set of at least 2^(N) different values,wherein the N switchable elements are configured such that:$f_{m,n}^{1} = \left( {\frac{2^{n}}{\Delta_{m}} + \frac{1}{f_{m,n}^{0}}} \right)^{- 1}$where f_(m) ¹ is a focal length of the n^(th) switchable element in them^(th) module when it is in its second state, where f_(m,n) ⁰ is a focallength of the n^(th) switchable element in the m^(th) module when the itis in its first state, where Δ_(m) is a constant for the m^(th) modulehaving the dimensions of length and independent of n, where n is aninteger between 0 and N−1, and m is an integer that is less than orequal to the number of modules in the device.
 26. The device of claim 25wherein Δ_(m)=f_(m,0) ¹, where f_(m,0) ¹ is the focal length for the 0^(th) switchable element in the m^(th) module when it is in its secondstate.
 27. The device of claim 25 wherein two or more switchableelements in the m^(th) module have substantially the same value fortheir first state focal lengths f_(m,n) ⁰ independent of n.
 28. Thedevice of claim 25 wherein all switchable elements in the m^(th) modulehave substantially the same value for their first state focal lengthsf_(m,n) ⁰ independent of n.
 29. The device of claim 25 wherein a portionof the switchable elements forms a lens stack.
 30. The device of claim25 wherein the N switchable elements are stacked coaxially.
 31. Thedevice of claim 30 wherein the N switchable elements are stacked suchthat each element is in approximate contact with any adjacent elements.32. A Digital Focus Lens System for providing an optical system having aplurality of selectable focal powers, comprising: a first switchableelement capable of being switched between a first-element first-stateand a first-element second-state; and and a second switchable elementcapable of being switched between a second-element first-state and asecond-element second-state; wherein the first switchable element has afocal length f_(m) ⁰ in the first-element first state and the secondswitchable element has the same focal length f_(m) ⁰ in thesecond-element first state, wherein the first and second switchableelements are in optical communication with each other such that each ofthem may contribute to a cumulative focal power, wherein, a first focalpower may be selected by activation of the first switchable element tothe first-element first-state and activation of the second switchableelement to the second-element first-state, wherein a second focal poweris selected by activation of the first switchable element to thefirst-element second-state and activation of the second switchableelement to the second-element first-state, wherein a third focal poweris selected by activation of the first switchable element to thefirst-element first-state and activation of the second switchableelement to the second-element second-state, and wherein a fourth focalpower is selected by activation of the first switchable element to thefirst-element second-state and activation of the second switchableelement to the second-element second-state, wherein the first and secondswitchable elements are two of N switchable elements in a module of adevice having M modules, where N is greater than or equal to two and Mis a number greater than or equal to 1; wherein each of the N switchableelements is switchable between discrete first and second states, whereina module focal length F_(m), or module focal power P_(m), of an m^(th)module are selectable from a set of 2^(N) focal lengths for theswitchable elements, where m is an integer between 1 and M, wherein theN switchable elements are configured such that a focal length F_(m) forthe m^(th) module can be selected from 2^(N−1) different possible valuesgiven by$F_{m} \in \left\{ {\frac{\Delta_{m}}{0},\frac{\Delta_{m}}{1},{\frac{\Delta_{m}}{2}\mspace{14mu}\ldots\mspace{14mu}\frac{\Delta_{m}}{2^{N} - 1}}} \right\}$where Δ_(m) is a constant for the m^(th) module having the dimension oflength.
 33. The device of claim 32 wherein the N switchable elements areconfigured such that a focal power P_(m) for the m^(th) module is givenby:$P_{m} \in \left\{ {\left( \frac{0}{\Delta_{m}} \right),\left( \frac{1}{\Delta_{m}} \right),{\left( \frac{2}{\Delta_{m}} \right)\mspace{14mu}\ldots\mspace{14mu}\left( \frac{\left( {2^{N} - 1} \right)}{\Delta_{m}} \right)}} \right\}$where Δ_(m) is a constant for the m^(th) module having the dimensions oflength.
 34. The system of claim 1 wherein the focal length f_(m) ⁰ isapproximately infinite.